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Feasible statistical modelling for extremes in ecology and finance

Statistical models for extreme value distributions have become increasingly popular in recent years as they provide a much better fit for data presenting some departures from normality than standardly normality-based statistical models. Typical drawbacks of application of normality based models are bias and underestimation of risks. This causes that application of those methods is unfeasible. On the other hand, many techniques developed for heavy tailed data are over complex and not very accurate. The aim of this project is to reduce this complexity of current developed extreme value theories by developing flexible and effective methods for extremes modeling and analysis. Especially, we aim to develop distribution sensitive, robust, and mid-sample techniques for  extreme valued processes, possibly dependent. This has a great potential for both finance and ecology.

We will illustrate the developed method on ecological and financial applications.

Partners

Prof. Mag. Dr. Milan Stehlik
IFAS, Johannes Kepler University in Linz, Austria
Linz Institute of Technology, JKU, Austria
Institute of Statistics, University of Valparaíso
milan.stehlik@jku.at
http://www.jku.at/ifas/content/e98868/index_html?team_view=&emp=e98868/employee_groups_wiss98983/employees99374

Assoc. Prof. Ph.D. Pavlina Jordanova
Associate Professor (Theory of Probability and Mathematical Statistics)
Faculty of mathematics and informatics
Shumen University, Bulgaria
p.jordanova@shu.bg
http://shu.bg/faculties/fmi/prepodavateli?faculty=fmi&teacherId=166#publications

Master Student Mag. Gerhard Holzknecht
IFAS, Johannes Kepler University in Linz, Austria
Linz Institute of Technology, JKU, Austria
gerhard.holzknecht@jku.at
http://www.jku.at/ifas/content/e98868/index_html?team_view=section&emp=e98868/employee_groups_wiss98983/employees340461

 

 

Publications

 1. Jordanova, P., Petkova, M.,  Stehlík, M. COMPOUND POWER SERIES DISTRIBUTION WITH NEGATIVE MULTINOMIAL SUMMANDS: CHARACTERISATION AND RISK PROCESS, RevStat Statistical Journal, Vol.18(1), pages 47-69, (2020) INST NACIONAL ESTATISTICA-INE, Lisbon, Portugal (Q4, WoS, Scopus и др.) ISSN: 1645-6726.

Click to access CompoundPowerSeriesDistribution.pdf

2. Jordanova, P., Kiselak, J., Stehlík, M. (2018) LOG-GAMMA MOTION AS FLEXIBLE MODEL FOR GENERALIZED INTEREST RATES, Stochastic Analysis, and Applications, 36(3), pages 373-392.

http://www.tandfonline.com/doi/full/10.1080/07362994.2017.1400917?scroll=top&needAccess=true

https://www.researchgate.net/publication/320774760_Log-Gamma_motion_as_flexible_model_for_generalized_interest_rates

3. Jordanova, P., Stehlík, M. (2018) ON MULTIVARIATE MODIFICATIONS OF CRAMER LUNDBERG RISK MODEL WITH CONSTANT INTENSITIES,  Stochastic Analysis and Applications, 36(5), pages 858-882.

https://www.tandfonline.com/doi/abs/10.1080/07362994.2018.1471403?journalCode=lsaa20

Click to access 1803.04518.pdf

4. Kiselak, J., Jordanova, P., Stehlík M. (2018) GENERALIZED INV-LOG-GAMMA-G PROCESSES, Stochastic Analysis and Applications, 36(6), pages 1053-1067.

https://www.tandfonline.com/doi/pdf/10.1080/07362994.2018.1524305?needAccess=true

https://www.researchgate.net/publication/328052549_Generalized_Inv-Log-Gamma-G_processes

5. Filus, J., Filus, L., Arnold, B.C., Jordanova, P.K., Soza, L.N., Lu, Y., Stehlíková, S., Stehlík, M., (2018) ON PARAMETER DEPENDENCE AND RELATED TOPICS: THE IMPACT OF  JERSY FILUS FROM GENESIS TO RECENT DEVELOPMENTS. Reliability Engineering. CRC Press, 143-172.

https://www.taylorfrancis.com/books/e/9781351130356/chapters/10.1201%2F9781351130363-8

6. Jordanova, P., Peteva, M. (2018) TAILS AND PROBABILITIES FOR EXTREME OUTLIERS, AIP Conference Proceedings. AIP Publishings 2025, pages 030002-1–030002-9.

https://aip.scitation.org/doi/pdf/10.1063/1.5064880?class=pdf

Click to access 1807.04751.pdf

7. Jordanova, P., Stehlík, M. (2018) P-THINNED GAMMA PROCESSES AND CORRESPONDING RANDOM WALK.  Finite Difference Methods: Theory and Applications, pages 297 — 304.

https://www.springer.com/gp/book/9783030115388?wt_mc=Internal.Event.1.SEM.ChapterAuthorCongrat

8. Jordanova, P. (2018) MERGING OF BIVARIATE COMPOUND POISSON RISK PROCESSES WITH SHOCKS, MATTEX 2018 conference proceedings, Vol. 1, pages 49-56, Shumen University Press, Bulgaria.

Click to access 49_56_mf-mattex-pjordanova-merging.pdf

9. Stehlík, M. (2018) EXACT DISTRIBUTIONS OF LR TESTS AND THEIR APPLICATIONS, MATTEX 2018 conference proceedings, 1, pages 37-38, Shumen University Press, Bulgaria.

Click to access 37_knla-mattexmst_abst.pdf

10. Stehlík, M., Maidana, J.P., Villarroel, Cl. N., Sepúlveda, M., Oliva, D., (2018) ON IGNORANCE REGIONS AND SPATIAL ASPECTS FOR SOUTH AMERICAN SEA LION (OTARIA BYRONIA) OPERATIONAL INTERACTION WITH THE ARTISAN GILLNET FISHERY IN CHILE, Finite Difference Methods: Theory and Applications, pages 92 — 101.

https://www.springer.com/gp/book/9783030115388?wt_mc=Internal.Event.1.SEM.ChapterAuthorCongrat

11. Soza, L., N., Jordanova, P., Nicolis, O.,  Strelec, L., Stehlík, M. (2019), SMALL SAMPLE ROBUST APPROACH TO OUTLIERS AND CORRELATION OF ATMOSPHERIC POLLUTION AND HEALTH EFFECTS IN SANTIAGO DE CHILE, Chemometrics and Intelligent Laboratory Systems, 185, pages 73-84.

https://www.sciencedirect.com/science/article/abs/pii/S0169743918304143

https://www.researchgate.net/publication/329895256_Small_sample_robust_approach_to_outliers_and_correlation_of_Atmospheric_Pollution_and_Health_Effects_in_Santiago_de_Chile

12. Stehlík, M., Soza, L.N., Fabiane, Z., Jirina, M., Jordanova, P., Arancibia, S.I.C., Kiselak, J. (2019), ON ECOLOGICAL ASPECTS OF DYNAMICS FOR ZERO SLOPE REGRESSION FOR WATER POLLUTION IN CHILE, Stochastic Analysis and Applications, 37(4), pages 574-601.

https://www.tandfonline.com/doi/abs/10.1080/07362994.2019.1592692?journalCode=lsaa20

13. Jordanova, P.K., Stehlik, M., LOGARITHM OF RATIOS OF TWO ORDER STATISTICS AND REGULARLY VARYING TAILS, In American Institute of Physics Conference Proceedings, Vol. 2164, No. 1, p. 030001-1 — 030001-9. 2019, American Institute of Physics Publishing, USA, ISSN:0094-243X, E-ISSN:1551-7616. (Scopus) . 

https://aip.scitation.org/doi/10.1063/1.5130791

Click to access 1904.07770.pdf

14. Jordanova P., Stehlík, M., IPO ESTIMATION OF THE HEAVINESS OF THE DISTRIBUTION BEYOND REGULARLY VARYING TAILS, Stochastic Analysis and Applications, vol. 38(1), pp. 76-96, ISSN: 0736-2994 eISSN: 1532-9356, TAYLOR & FRANCIS INC (Q3) WoS, Scopus 

https://www.tandfonline.com/doi/abs/10.1080/07362994.2019.1647786?journalCode=lsaa20

https://www.researchgate.net/publication/334808289_IPO_estimation_of_heaviness_of_the_distribution_beyond_regularly_varying_tails

15. Mantalos, P., Karagrigoriou, A., Strelec, L., Jordanova, P., Hermann, Ph., Kiselak, J., Hudak, J., Stehlík, M., ON IMPROVED VOLATILITY MODELLING BY FITTING SKEWNESS IN ARCH MODELS,  Journal of Applied Statistics, vol. 47(6), pp. 1031-1063, ISSN: 0266-4763, eISSN: 1360-0532, TAYLOR & FRANCIS LTD, England (Q3) WoS, Scopus 

https://www.tandfonline.com/doi/abs/10.1080/02664763.2019.1671323

https://www.researchgate.net/publication/335681443_On_improved_volatility_modelling_by_fitting_Skewness_in_ARCH_models

16. Jordanova, P., (2019) PROBABILITIES FOR p-OUTSIDE VALUES – PARTICULAR CASES, AIP Conference Proceedings, 2172, pages 100004-1–100004-9.

https://aip.scitation.org/doi/pdf/10.1063/1.5133597

17. Jordanova, P., (2019) PROBABILITIES FOR p-OUTSIDE VALUES – GENERAL PROPERTIES, AIP Conference Proceedings, 2164(1), pages 020002-1 — 020002-11.

https://aip.scitation.org/doi/abs/10.1063/1.5130789

18. Stehlik M., Kiselak J., Vaiciulis M., Jordanova P., Soza L., Fabian Z., Hermann P., Strelec L., Rivera A., Girard S., Torres Leiva S. (2020) PRIORITY STATEMENT AND SOME PROPERTIES OF T-LGHILL ESTIMATOR, Extremes, vol. 23, pages 493-499.

https://link.springer.com/article/10.1007/s10687-020-00375-2

19. Jordanova, P., PROBABILITIES FOR P-OUTSIDE VALUES AND HEAVY TAILS, Konstantin Preslavsky Publishing House, Shumen, Bulgaria, 2020, ISBN 978-619-201-381-3(print), ISBN 978-619-201-401-8(online) 178 pages

Click to access contents-and-references.pdf

20. Jordanova, P.K., Stehlik, M., DISTRIBUTION SENSITIVE ESTIMATORS OF THE INDEX OF REGULAR VARIATION BASED ON RATIOS OF ORDER STATISTICS, (accepted)

Click to access 2007.14842.pdf

21. M. Stehlik, L. M. Grilo, P.K. Jordanova (2020) EDITORIAL TO SPEDIAL ISSUE V WCDANM 2018, Special issue Advances in Computational Data Analysis, Journal of Applied Statistics, vol. 47(13-15), pages 2289-2298, DOI: 10.1080/02664763.2020.1818489, ISSN: 0266-4763 eISSN: 1360-0532, TAYLOR & FRANCIS INC (Q3) WoS, Scopus.

https://www.tandfonline.com/doi/pdf/10.1080/02664763.2020.1818489?needAccess=true

22. M. Stehlik, L. Strelec, G. Holzknecht, J. Kiselak, “Analysis of ECB Consolidated Banking Data and covid19-outbreaks perspectives for negative interest rates”, (accepted).

https://www.researchgate.net/publication/344319795_Analysis_of_ECB_Consolidated_Banking_Data_and_covid19-outbreaks_perspectives_for_negative_interest_rates

Talks

1. Pavlina Jordanova, Seminar – “Multivariate” modifications of the Cramer-Lundberg model, JKUInstitut für Angewandte Statistik, Science Park 2, ZG 0074, 24.05.2018, 16:30.

https://www.jku.at/institut-fuer-angewandte-statistik/forschung/forschungsseminar/

2. Pavlina Jordanova, “Tails and probabilities for extreme outliers”, AMiTaNS’2018, 20.06.2018 – 25.06.2018, Albena, Bulgaria.

http://2018.eac4amitans.eu

3. Milan Stehlik, “On Statistical Invariants, Groups and Broken Symmetries for Algebraic Confidence Covers “, AMiTaNS’2018, 20.06.2018 – 25.06.2018, Albena, Bulgaria.

http://2018.eac4amitans.eu

4. Pavlina Jordanova, “P-thinned Gamma process and corresponding random walk”, Seventh Conference on Finite Difference Methods: Theory and Applications
(FDM: T&A’2018), June 11-16, 2018 Lozenetz, Bulgaria.

http://parallel.bas.bg/dpa/FDM2018/

5. Milan Stehlik, Seventh Conference on Finite Difference Methods: Theory and Applications (FDM: T&A’2018), June 11-16, 2018 Lozenetz, Bulgaria.

http://parallel.bas.bg/dpa/FDM2018/

6. Pavlina Jordanova, “Merging of bivariate Compound Poisson risk processes with shocks”, MATTEX 2018, the Scientific session “Extreme value analysis, random processes and applications”,  October 25-27, 2018,  Faculty of Mathematics and Informatics and Faculty of Technical Sciences, Shumen University, Bulgaria.

http://info.fmi.shu-bg.net/mattex/mattex.htm

7. Milan Stehlik. “Exact distributions of LR tests and their applications”, MATTEX 2018, the Scientific session “Extreme value analysis, random processes and applications”,  October 25-27, 2018,  Faculty of Mathematics and Informatics and Faculty of Technical Sciences, Shumen University, Bulgaria.

http://info.fmi.shu-bg.net/mattex/mattex.htm

8. Pavlina Jordanova, “Tails and probabilities for p-outliers”, Seminar – Mathematics, Faculty of Mathematics and Informatics, 02.04.2019/11:00/K3-V-505 Konstantin Preslavsky University of Shumen, Bulgaria.

http://info.fmi.shu-bg.net/pages.php?p_id=37

9. Pavlina Jordanova, “Tails and probabilities for p-outliers”, National Seminar on Probability and Statistics, 10.04.2019/14:00, Room 403, Institute of Mathematics and Informatics, Bulgarian Academy of Science,  Bulgaria.

http://www.math.bas.bg/~statlab/semi2012.html

10. Pavlina Jordanova, “Tails and probabilities for p-outliers”, The 22nd Conference of the Romanian Society of Probability and Statistics Bucharest, May 10-11, 2019.

http://www.spsr.ase.ro/media/Default/spsr2019/programspsr.pdf

11. Pavlina Jordanova, “Probabilities for p-Outliers – General Properties”, AMiTaNS’2019, 20.06.2019 – 25.06.2019, Albena, Bulgaria.

http://2019.eac4amitans.eu/

12. Pavlina Jordanova, “Logarithms of Ratios of Two Order Statistics and Regularly Varying Tails”, AMiTaNS’2019, 20.06.2019 – 25.06.2019, Albena, Bulgaria.

http://2019.eac4amitans.eu/

13. Milan Stehlik. “Extracting extreme aspects from series of random dynamical system”, National Seminar on Probability and Statistics, 31.07.2019/15:00, Room 403, Institute of Mathematics and Informatics, Bulgarian Academy of Science,  Bulgaria.

http://www.math.bas.bg/~statlab/semi2012.html

14. Pavlina Jordanova, “Distribution sensitive estimators of the index of regular variation based on ratios of order statistics”, AMiTaNS’2020, 24.06.2020 – 29.06.2020, Albena, Bulgaria.

http://2020.eac4amitans.eu/

15. Milan Stehlik, “Analysis of ECB Consolidated Banking Data and
covid19-outbreaks perspectives for negative interest rates”, AMiTaNS’2020, 24.06.2020 – 29.06.2020, Albena, Bulgaria.

http://2020.eac4amitans.eu/

16. Pavlina Jordanova, “Ratios of order statistics and regularly varying tails”, VII Workshop Computational data Analysis and Numerical Methods, 10-12 September 2020, Polytechnic Institute of Tomar, Tomar, Portugal.

http://www.wcdanm.ipt.pt/pt/program/vii_wcdanm_program/

http://www.wcdanm.ipt.pt/pt/program/book_of_abstracts/

17. Milan Stehlik, “Modelling and prediction of COVID-19 outbreaks”, VII Workshop Computational data Analysis and Numerical Methods, 10-12 September 2020, Polytechnic Institute of Tomar, Tomar, Portugal.

http://www.wcdanm.ipt.pt/pt/program/book_of_abstracts/